Both areas have been big reasons for optimism about sales growth for many tech suppliers

China and cloud computing have been the biggest reasons for optimism about sales growth for many technology suppliers. But Intel Corp. on Thursday raised worries about both, sending its share price tumbling and adding to fears rocking the stock market.

The giant chip maker issued a financial projection for the first fiscal quarter that was lower than analysts expected, after subtracting the effect of an extra workweek in the period and the impact of a recent acquisition. Intel executives attributed its low expectation largely...